Contact Geometry and Thermodynamics **of** Black Holes in AdS

**equations**

**of**

**state**of general black holes in AdS are shown to emerge from the high temperature ideal gas limit

**equation**s, via suitable deformations induced by contact vector fields. Expand abstract.

**of**extended phase space thermodynamics

**of**black holes in Anti de Sitter (AdS) space-time, from the contact geometry point

**of**view. Thermodynamics

**of**black holes can be understood within the framework

**of**contact geometry as flows

**of**vector fields generated by Hamiltonian functions on equilibrium submanifolds in the extended phase space, that naturally incorporates the structure

**of**a contact manifold. Deformations induced by the contact vector fields are used to construct various maps among thermodynamic quantities. Thermodynamic variables and

**equations**

**of**

**state**

**of**Schwarzschild black holes are mapped to that

**of**Reissner-Nordstrom black holes in AdS, with charge as the deformation parameter. In addition, the

**equations**

**of**

**state**

**of**general black holes in AdS are shown to emerge from the high temperature ideal gas limit equations, via suitable deformations induced by contact vector fields. The Hamilton-Jacobi formalism analogous to mechanics is set up and the corresponding characteristic curves

**of**contact vector fields are explicitly obtained, to model thermodynamic processes

**of**black holes. Extension to thermodynamic cycles in this framework is also discussed.

4/10 relevant

arXiv

Three-dimensional **equations** **of** generalized dynamics of 18-fold symmetry
soft-matter quasicrystals

**equations**present some important meaning in the study on thermodynamics

**of**the matter which is also introduced. Expand abstract.

**of**governing

**equations**

**of**generalized dynamics

**of**18-fold symmetry soft-matter quasicrystals, according to the dynamics basis there are first and second phason elementary excitations apart from phonons and fluid phonon. In the derivation, the group representation theory is a key point. The complete form

**of**the theory includes an

**equation**

**of**

**state**. The governing

**equations**present some important meaning in the study on thermodynamics

**of**the matter which is also introduced.

4/10 relevant

arXiv

A unique **equation** **of** **state** for the universe evolution from AdS$_5$
space-time

**of**the universe. The positive $\Lambda$ case yields a bounce cosmological model. In the negative five-dimensional cosmological constant case, the scale factor is obtained as $a(t)\sim\sqrt[]{\sinh t}$, which is able to describe not only the late-time cosmic acceleration but also the non-accelerated stages

**of**the cosmic expansion in a continuous form. This solution together with the extra-dimensional scale factor solution yields the material content

**of**the model to be remarkably related through an

**equation**

**of**

**state**analogous to the renowned MIT bag model

**equation**

**of**

**state**for quark matter $p=(\rho-4B)/3$. In our case, $\rho=\rho_m+B$, with $\rho_m$ being the energy density

**of**relativistic and non-relativistic matter and $B=\ \Lambda /16\pi$ represents the bag energy constant, which plays the role

**of**the dark energy in the four-dimensional universe, with $\Lambda$ being the cosmological constant

**of**the AdS$_5$ space-time. Our model satisfactorily fits the observational data for the low redshift sample

**of**the experimental measurement

**of**the Hubble parameter, which resulted in $H_0=72.2^{+5.3}_{-5.5}$km s$^{-1}$ Mpc$^{-1}$.

7/10 relevant

arXiv

Analytic Fluid Approximation for Warm Dark Matter

**equation**

**of**

**state**we are able to analytically compute the energy density and pressure evolution. Expand abstract.

**of**the velocity for a massive particle, along with the

**equation**

**of**

**state**we are able to analytically compute the energy density and pressure evolution. Therefore, is easy to compute the perturbation

**equations**for any massive decoupled particle, i.e. warm dark matter (WDM) or neutrinos, treated as fluid. Using this approach we analytical calculate the moment when the WDM stop being relativistic, a_nr, which is just 15% difference with respect to the exact Boltzmann solution. Using the fluid approximation the matter power spectrum is computed fast and with great accuracy, the cut-off in structure formation due to the free-streaming, lambda_fs,

**of**the particle, characteristic for a WDM particle, is replicated in both matter power spectrum and halo mass function, in which we found up to 30% correction on the Jeans mass. We also show that the matter power can be computed using a fitting formula that involves only the cut-off scale, k_fs. This formulation can be integrated in comprehensive numerical modeling reasonable increasing the performance in the calculations.

4/10 relevant

arXiv

An **equation** **of** **state** for high pressure-temperature liquids (RTpress) with application to MgSiO3 melt

**Equation**

**of**

**State**(EOS) models to predict the early evolution of planetary interiors. Expand abstract.

**of**molten silicates at extreme conditions are crucial for understanding the early evolution

**of**Earth and other massive rocky planets, which is marked by giant impacts capable

**of**producing deep magma oceans. Cooling and crystallization

**of**molten mantles are sensitive to the densities and adiabatic profiles

**of**high-pressure molten silicates, demanding accurate

**Equation**

**of**

**State**(EOS) models to predict the early evolution

**of**planetary interiors. Unfortunately, EOS modeling for liquids at high P-T conditions is difficult due to constantly evolving liquid structure. The Rosenfeld-Tarazona (RT) model provides a physically sensible and accurate description

**of**liquids but is limited to constant volume heating paths (Rosenfeld and Tarazona, 1998). We develop a high P-T EOS for liquids, called RTpress, which uses a generalized Rosenfeld-Tarazona model as a thermal perturbation to isothermal and adiabatic reference compression curves. This approach provides a thermodynamically consistent EOS which remains accurate over a large P-T range and depends on a limited number

**of**physically meaningful parameters that can be determined empirically from either simulated or experimental datasets. As a first application, we model MgSiO3 melt representing a simplified rocky mantle chemistry. The model parameters are fitted to the MD simulations

**of**both Spera et al. (2011) and de Koker and Stixrude (2009), recovering pressures, volumes, and internal energies to within 0.6 GPa, 0.1 Å^3, and 6 meV per atom on average (for the higher resolution data set), as well as accurately predicting liquid densities and temperatures from shock-wave experiments on MgSiO3 glass. The fitted EOS is used to determine adiabatic thermal profiles, revealing the approximate thermal structure

**of**a fully molten magma ocean like that

**of**the early Earth. These adiabats, which are in strong agreement for both fitted models, are shown to be sufficiently steep to produce either a center-outwards or bottom-up style

**of**crystallization, depending on the curvature

**of**the mantle melting curve (liquidus), with a high-curvature model yielding crystallization at depths

**of**roughly 80 GPa (Stixrude et al., 2009) whereas a nearly-flat experimentally determined liquidus implies bottom-up crystallization (Andrault et al., 2011).

10/10 relevant

EarthArXiv

Measuring the neutron star **equation** **of** **state** with gravitational waves:
the first forty binary neutron star mergers

**equation**

**of**

**state**. We can measure the

**equation**

**of**

**state**by analyzing the tidal interactions between neutron stars, which is quantified by the tidal deformability. Multiple merger events are required to probe the

**equation**

**of**

**state**over a range

**of**neutron star masses. The more events included in the analysis, the stronger the constraints on the

**equation**

**of**

**state**. In this paper, we build on previous work to explore the constraints that LIGO and Virgo are likely to place on the neutron star

**equation**

**of**

**state**by combining the first forty binary neutron star detections, a milestone we project to be reached during the first year

**of**accumulated design-sensitivity data. We carry out Bayesian inference on a realistic mock dataset

**of**binaries to obtain posterior distributions for neutron star tidal parameters. In order to combine posterior samples from multiple observations, we employ a random forest regressor, which allows us to efficiently interpolate the likelihood distribution. Assuming a merger rate

**of**1540 Gpc$^{-3}$ yr$^{-1}$ and a LIGO-Virgo detector network operating for one year at the sensitivity

**of**the third-observation run, plus an additional eight months

**of**design sensitivity, we find that the radius

**of**a 1.4 $M_\odot$ neutron star can be constrained to $\sim 10$% at 90% confidence. At the same time, the pressure at twice the nuclear saturation density can be constrained to $\sim 45$ % at 90% confidence.

7/10 relevant

arXiv

Rotating neutron stars with non-barotropic thermal profile

**equations**

**of**

**state**. Expand abstract.

**of**axisymmetric, stationary, differentially rotating neutron stars were constructed under the strong assumption

**of**barotropicity, where a one-to-one relation between all thermodynamic quantities exists. This implies that the specific angular momentum

**of**a matter element depends only on its angular velocity. The physical conditions in the early stages

**of**neutron stars, however, are determined by their violent birth processes, typically a supernova or in some cases the merger

**of**two neutron stars, and detailed numerical models show that the resulting stars are by no means barotropic. Here, we construct models for stationary, differentially rotating, non-barotropic neutron stars, where the

**equation**

**of**

**state**and the specific angular momentum depend on more than one independent variable. We show that the potential formulation

**of**the relativistic Euler

**equation**can be extended to the non-barotropic case, which, to the best

**of**our knowledge, is a new result even for the Newtonian case. We implement the new method into the XNS code and construct equilibrium configurations for non-barotropic

**equations**

**of**

**state**. We scrutinize the resulting configurations by evolving them dynamically with the numerical relativity code BAM, thereby demonstrating that the new method indeed produces stationary, differentially rotating, non-barotropic neutron star configurations.

4/10 relevant

arXiv

kiloHertz gravitational waves from binary neutron star remnants: time-domain model and constraints on extreme matter

**equation**

**of**

**state**at extreme densities using the quasiuniversal relations deduced from numerical-relativity simulations. Expand abstract.

**of**a neutron star merger is an anticipated loud source

**of**kiloHertz gravitational waves that conveys unique information on the

**equation**

**of**

**state**

**of**hot matter at extreme densities. Observations

**of**such signals are hampered by the photon shot noise

**of**ground-based interferometers and pose a challenge for gravitational-wave astronomy. We develop an analytical time-domain waveform model for postmerger signals informed by numerical relativity simulations. The model completes effective-one-body waveforms for quasi-circular nonspinning binaries in the kiloHertz regime. We show that a template-based analysis can detect postmerger signals with a minimal signal-to-noise ratios (SNR)

**of**8, corresponding to GW170817-like events for third-generation interferometers. Using Bayesian model selection and the complete inspiral-merger-postmerger waveform model it is possible to infer whether the merger outcome is a prompt collapse to a black hole or a remnant star. In the latter case, the radius

**of**the maximum mass (most compact) nonrotating neutron star can be determined to kilometer precision. We demonstrate the feasibility

**of**inferring the stiffness

**of**the

**equation**

**of**

**state**at extreme densities using the quasiuniversal relations deduced from numerical-relativity simulations.

4/10 relevant

arXiv

Renormalization group approach to the normal phase **of** 2D Fermi gases

**equation**

**of**

**state**in trapped gases in the balanced regime, showing that these results are consistent with logarithmic corrections in the equation of state. Expand abstract.

**of**short-range, attractive interactions on the properties

**of**balanced 2D Fermi gases in the non-superfluid (normal) phase. Our approach combines the renormalization group (RG) with perturbation theory, yielding observables such as the

**equation**

**of**

**state**and compressibility. We find good agreement with recent experiments that measured the

**equation**

**of**

**state**in trapped gases in the balanced regime, showing that these results are consistent with logarithmic corrections in the

**equation**

**of**

**state**.

7/10 relevant

arXiv

**Equation** Systems **of** Generalized Hydrodynamics for Soft-Matter
Quasicrystals

**equations**

**of**the dynamics are reported in this letter. Expand abstract.

**equation**systems

**of**generalized hydrodynamics, or generalized dynamics for simplicity, for soft-matter quasicrystals were established. Considering the fluidity

**of**the matter with high order we introduced a new elementary excitation---fluid phonon to the quasicrystals, and the

**equation**

**of**

**state**is necessary and introduced too. By considering other two elementary excitations---phonons and phasons, a theory---generalized hydrodynamics for soft-matter quasicrystals is set up, in which the governing

**equations**

**of**the dynamics are reported in this letter.

4/10 relevant

arXiv