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One of the more exciting things to emerge from black hole thermodynamics in the past 10 years is the understanding that black holes can undergo a broad range of chemical-like phase transitions, including liquid-gas phase transitions, triple points, superfluid transitions, polymer-type transitions, and exhibit critical behaviour. It is even possible to consider black holes as the working material for heat engines. The efficiencies for a variety of black holes can be calculated and compared against each other.

In this talk I will discuss the connection between critical behaviour and the efficiency of black hole heat engines. I first consider the heat capacity of static black holes at constant volume such that Cv=0 Using the near critical expansion of the equation of state, the coefficients appearing in this expansion can be found from an engine cycle placed along a critical point on a PV plot. 

I will discuss the importance and applications of the simplifications made, along with how this result allows one to go from the near critical expansion of the equation of state directly to a conclusion about the behaviour of a heat engine near the critical point.

CAP Virtual Congress 2021

Black Hole Heat Engines and Critical Behaviour

critical behaviour

heat engine

black hole

**WELCOME TO THE 2021 CAP VIRTUAL CONGRESS UNDERLINE PLATFORM**

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technical paper

One of the more exciting things to emerge from black hole thermodynamics is that black holes can form the working material for heat engines. I explore the connection between the critical behaviour of black holes and their efficiency as heat engines over a range of dimensions and for a variety of theories of gravity. 

I first show that their efficiency as heat engines near the critical point can be written in general dimensions in terms of the variables characterizing the geometry of the cycle and the critical exponents. Engines near the critical point approach the Carnot efficiency, with the rate of approach determined by the universality class of the black hole. I will specifically consider a broad range of charged black holes, Lovelock black holes, and black holes with isolated critical points. I will then discuss work in progress exploring this formalism for black holes whose specific heat at constant volume is nonzero, applying it to examples such as rotating black holes and STU black holes.

Efficiency of Black Hole Heat Engines and Universality

The common picture of a binary black hole merger is the “pair of pants” diagram for the event horizon. However, in many circumstances, such as those encountered in numerical simulations, the event horizon may be ill-suited and it is more practical to work with quasi-local definitions of black hole boundaries, such as marginally outer trapped surfaces (MOTS). The analog of the pair of pants diagram for the apparent horizons remains to be fully understood. In this talk, I will discuss the complete picture for the merger of two axisymmetric black holes. I will begin by introducing new classes of MOTS present in Brill-Lindquist initial data. I will then discuss the role played by these and related surfaces in understanding the final fate of the apparent horizons of the initial two participants in the merger.

The fate of apparent horizons in a binary black hole merger

I describe the first investigation of the holographic complexity conjectures for rotating black holes. Exploiting a simplification that occurs for equal-spinning odd dimensional black holes, I demonstrate a relationship between the complexity of formation and the thermodynamic volume associated with the black hole. This result suggests that it is thermodynamic volume and not entropy that governs the complexity of formation in both the Complexity Equals Volume and Complexity Equals Action proposals. This proposal reduces to known results involving the entropy in settings where the thermodynamic volume and entropy are not independent, but has much broader scope. Assuming the validity of a conjectured inequality for thermodynamic volume, this result suggests the complexity of formation is bounded from below by the entropy for large black holes.

Holographic Complexity and Black Hole Thermodynamic Volume

We carry out the first investigation of the entanglement and mutual information harvesting protocols for detectors moving on freely falling trajectories that cross the horizon of a black hole. We consider two pointlike Unruh-DeWitt detectors in different combinations of free-falling and static trajectories in (1+1)-dimensional Schwarzschild black hole spacetime and compare the results. We find that (i) correlations harvested between free-falling and static detectors are always less than those of the familiar two-static-detector case (ii) there is a large kinematic component to the correlations; (ii) correlations can be harvested purely from the quantum vacuum, with evidence that this is possible even when the detectors are causally disconnected by the event horizon; (iii) the previously known `entanglement shadow' near the horizon is indeed absent for the two free-falling-detector case since the relative gravitational redshift of the detectors remains finite as the horizon is crossed, in accordance with the equivalence principle.

Harvesting Entanglement inside a Black Hole

Magnetic Resonance Imaging (MRI) detects signal from hydrogen nuclei in biological tissue. MRI requires a homogeneous static magnetic field to generate artifact-free images. The subject is spatially encoded with magnetic field gradients. The signal is acquired in the frequency domain and the image is reconstructed by inverse Fourier transform. Objects with high magnetic susceptibility, such as MRI-safe metallic implants, distort the surrounding magnetic field. This leads to severe artifacts that appear as signal voids in the conventional MRI images, due to rapid intravoxel dephasing, in addition to misregistration of frequencies to position.
Pure phase encoding techniques with short encoding times are largely immune to magnetic field inhomogeneity artifacts. This is because the constant signal evolution times can be sufficiently short that no appreciable dephasing has occurred. High quality artifact-free MRI images were acquired with pure phase encoding techniques, from which the magnetic field distribution around the metal was derived. This approach was compared with conventional MRI methods, which failed to map the magnetic field in high susceptibility regions. Although it is challenging to apply the proposed method in a routine clinical MRI scan, the measured magnetic field distribution could enable the development of novel nonlinear encoding techniques, where the metal induced magnetic field distortion is exploited to provide spatial information.

Mapping Magnetic Field Around Metal with Pure Phase Encoding Magnetic Resonance Imaging

Calcium (Ca) is an essential mineral in the body that helps maintain healthy bone density. Dysreguation of Ca can result in serious health issues and a reliable and efficient method of identifying changes in bone mineral balance can help to provide eaarly diagnosis of deteriorating bone health. The objective of this project is to investigate the application of naturally occurring Ca isotope abundance variations to understand biological processes, including biomineralization. This is because the kinetics underlying metabolic processes that involve Ca are mass dependent and will redistribute the abundances of naturally occuring, stable Ca isotopes. Thus, a careful measurement of Ca isotopic composition of the Ca pools in the body (i.e. bone, blood, and urine) can provide unique insight into the disruption of Ca metabolism. The extent of natural variations of stable Ca isotopes in the human metabolism is limited with a relative natural variation of less than 0.5% in the 44Ca/40Ca isotope amount ratio. Therefore, reliable measurement of Ca isotopic composition has remained very challenging, especially considering low Ca levels and significant procedural blank levels. The goal of this project was so develop a reliable and accurate analytical measurement procedures specifically for small amounts (approx. 1 µg) of Ca in biological materials.

In this study the extraction and isolation of calcium from a diverse set of biological matrices was optimized for low procedural blanks and separation from matrix elements and isobaric interferences such as Na, Mg, K, Mg, Ti, Fe, Ba. A 42Ca–48Ca double spike (DS) was applied to correct for potential isotopic fractionation during sample preparation and measurement. Ca isotope abundance analysis was performed using a multicollector thermal ionization mass spectrometer. The measurement procedure enabled processing of total Ca amounts of 1000 ng, with a total procedural blank of <10 ng and enabled measurement of the Ca isotopic compositions of the reference materials NIST SRM 1400 (bone ash), NIST SRM 1486 (bone meal) and IAPSO (seawater).

Dorothy Walls1, Anika Retzmann2, Kerri A. Miller1, Johanna Irrgeher1,2, Thomas Prohaska1,2, Michael Wieser1

1 Department of Physics and Astronomy, University of Calgary, Canada.

2 Chair of General and Analytical Chemistry, Montanuniversität Leoben, Austria.

Measuring calcium isotopic composition in the body to understand metabolic processes.

In the case of binary black hole mergers, the surface of most obvious interest, the Event Horizon, is often computationally difficult to locate. Instead, it is useful to turn to quasi-local characterizations of black hole boundaries, such as Marginally Outer Trapped Surfaces (MOTS), which are defined for a single time slice of the spacetime, and the outer-most of which is the apparent horizon. In this talk, I will describe ongoing work focused on understanding MOTS in the interior of a five-dimensional black hole; both static and rotating. Similar to the four-dimensional Schwarzschild case previously studied, we find examples of self-intersecting MOTS with an arbitrary number of self-intersections. This provides further support that self-intersecting behavior is rather generic. I will also discuss the second stage of our research, which is for a rotating 5D black hole spacetime. These two cases fit into a larger project involving exploration of the generality of self-intersecting behaviour in MOTS, within spacetimes of increasing diversity.

Marginally Outer Trapped (Open) Surfaces in 4+1 Dimensional Spacetimes

**Introduction:** pHi is a hallmark of altered cellular function in the tumour microenvironment and its response to therapies. One of the main acid-extruding membrane transport proteins in cells is the Na+/H+ exchanger isoform 1 (NHE1). Chemical exchange saturation transfer (CEST) MRI uniquely images pHi. In CEST-MRI, contrast is produced by exciting exchangeable tissue protons at their specific absorption frequency and observing the transfer of magnetization to bulk tissue water. Amine and amide concentration-independent detection (AACID) is a ratiometric approach that uses the distinctive sensitivity of amine and amide protons to CETS contrast. The AACID value inversely relates to tissue pHi. One way to achieve tumour acidification as a therapeutic strategy is by blocking the NHE1 transporter. Cariporide is a potent inhibitor of NHE1. We have shown that cariporide can selectively acidify U87MG glioma in mice. The goal of this study was to determine whether cariporide also selectively acidifies a rat C6 glioma tumour model immediately following injection by mapping tumour pHi.
**Methods:** A 2μL suspension of 10^6 C6 glioma cells were injected into the right frontal lobe of six 8-week-old male rats. To evaluate the effect of cariporide on tumour pHi, rats received an IP injection of the drug (6mg/kg in 2ml) two weeks after tumour implantation. They received the drug inside a 9.4T scanner to measure the change in pHi following injection. 
**Results:** Five minutes after injection we started collecting CEST-MRI for 3 hours. For data analysis, we compared the first maximum change in AACID value post-injection with the pre-injection value. Approximately 60 minutes after injection, the average AACID value in the tumour significantly increased (p<0.05). The average AACID value in tumour post-injection was 5.4% higher compared to pre-injection corresponding to a 0.26 lower pHi. The average AACID value in contralateral tissue also increased in a similar way.
**Conclusion:** We did not observe selective tumour acidification following injection as was observed in the previous study. The reason for this discrepancy is currently unknown but may be related to potential differences in tumour vasculature that may limit the ability of cariporide to infiltrate the tumour. Future work includes increasing cariporide dose and modifying our quantification method to increase the temporal stability of the AACID measurement.

Cariporide Effects on Intracellular pH (pHi) Using CEST-MRI in Rat Model of Glioblastoma

Graphene field effect transistors (GFETs) have an enormous potential for the development of next-generation gas sensors, but more efforts are required to improve their sensitivity and selectivity. In this talk we discuss UV illumination as a promising method to enhance the performance of GFETs for the detection and recognition of analytes such as ethanol, water vapor and dimethyl methylphosphonate (DMMP), a molecule with structural similarities to nerve agents such as sarin. We show that illuminating the devices in operando with a UV LED results in both improved sensitivity and selectivity. By monitoring the sensing response of the GFETs as a function of gate voltage, we directly demonstrate that a shift in the Dirac point due to the optical doping is associated with the increased sensitivity. Moreover, we discuss how the substrate and fabrication residues on the surface of the graphene sensors can play a role in modifying the sensing performance.

Optically enhanced gas sensing performance of graphene field effect transistors

High harmonic generation (HHG) in gasses has become a method of choice among table-top extreme ultraviolet (XUV) sources. In order to generate higher photon energies from this process, many strategies can be implemented, including red-shifting and compressing the driver pulses. Here, we propose a new approach for inducing a red-shift to driver pulses and compressing them to few-cycle durations in a single stage. This method uses the recently discovered multidimensional solitary states (MDSS) pulses that result from the nonlinear Raman process in gas-filled hollow-core fibers. It has a few key advantages: 1) MDSS are created from relatively long pulses, making this method suitable for any laser source offering sub-picosecond pulses. 2) The MDSS pulses can be compressed by simple propagation through glass. 3) In contrast with commonly-used optical parametric amplifiers, the induced red-shift can be modest, allowing to reach a target XUV photon energy while minimizing the detrimental effects of long driver wavelengths on HHG efficiency. 
To produce MDSS pulses, the output pulses of a Titanium-Sapphire system are stretched to 400 fs and coupled to a hollow-core fiber filled with nitrogen. In the fiber, intermodal nonlinear processes occur which lead to the red-shifted MDSS pulses. Then, CaF2 plates inserted into the beam path compress the pulses down to 12 fs and these are sent to an argon-filled cell where HHG occurs. From this simple apparatus, the HHG spectrum is expanded to cover the M$_{2,3}$ edge of cobalt and $10^9$ photons/second are generated at 60 eV. This significant XUV photon flux allows for the implementation of X-ray resonant magnetic scattering measurements on a cobalt/platinum ferromagnet, an example of photon-hungry application. Although such flux has previously been generated in a different gas from the direct output of the same laser system, the conversion efficiency of our approach is one order of magnitude higher as it allows to reach the target photon energy by generating harmonics in argon, a gas that offers a large generation efficiency. Due to its simplicity and versatility, our approach can readily be adapted to different applications and could be particularly interesting for high power Ytterbium laser systems offering sub-picosecond pulses.

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Black Hole Heat Engines and Critical Behaviour

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