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José P. S. Lemos

Publications and source records attributed to José P. S. Lemos.

At least 73 records · Page 4Linked to original sources
arXiv2016

Vacuum polarization in asymptotically Lifshitz black holes

There has been considerable interest in applying the gauge/gravity duality to condensed matter theories with particular attention being devoted to gravity duals (Lifshitz spacetimes) of theories that exhibit anisotropic scaling. In this context, black hole solutions with Lifshitz asymptotics have also been constructed aiming at incorporating finite temperature effects. The goal here is to look at quantum polarization effects in these spacetimes, and to this aim, we develop a way to compute the coincidence limit of the Green's function for massive, non-minimally coupled scalar fields, adapting to the present situation the analysis developed for the case of asymptotically anti de Sitter black holes. The basics are similar to previous calculations, however in the Lifshitz case one needs to extend previous results to include a more general form for the metric and dependence on the dynamical exponent. All formulae are shown to reduce to the AdS case studied before once the value of the dynamical exponent is set to unity and the metric functions are accordingly chosen. The analytical results we present are general and can be applied to a variety of cases, in fact, to all spherically symmetric Lifshitz black hole solutions. We also implement the numerical analysis choosing some known Lifshitz black hole solutions as illustration.

gr-qc↗
arXiv2016

Entropy of extremal black holes: horizon limits through charged thin shells, a unified approach

Using a unified approach we study the entropy of extremal black holes through the entropy of an electrically charged thin shell. We encounter three cases in which a shell can be taken to its own gravitational or horizon radius and become an extremal spacetime. In case 1, we use a non extremal shell, calculate all the thermodynamics quantities including the entropy, take it to the horizon radius, and then take the extremal limit. In case 2, we take the extremal limit and the horizon radius limit simultaneously, i.e., as the shell approaches its horizon radius it also approaches extremality. In case 3, we build first an extremal shell, and then take its horizon radius. We find that the thermodynamic quantities in general have different expressions in the three different cases. The entropy is the Bekenstein-Hawking entropy $ S=A_+/4$ (where $A_+$ is the horizon area) in cases 1 and 2, and in case 3 it can be any well-behaved function of $A_+$. The contributions from the various thermodynamic quantities for the entropy in all three cases are distinct. Indeed, in cases 1 and 2 the limits agree in what concerns the entropy but they disagree in the behavior of all other thermodynamic quantities. Cases 2 and 3 disagree in what concerns the entropy but agree in the behavior of the local temperature and electric potential. Case 2 is in a sense intermediate between cases 1 and 3. Our approach sheds light on the extremal black hole entropy issue.

hep-th↗
arXiv2016

Regular nonminimal magnetic black holes in spacetimes with a cosmological constant

We consider new regular exact spherically symmetric solutions of a nonminimal Einstein--Yang-Mills theory with a cosmological constant and a gauge field of magnetic Wu-Yang type. The most interesting solutions found are black holes with metric and curvature invariants that are regular everywhere, i.e., regular black holes. We set up a classification of the solutions according to the number and type of horizons. The structure of these regular black holes is characterized by four specific features: a small cavity in the neighborhood of the center, a repulsion barrier off the small cavity, a distant equilibrium point, in which the metric function has a minimum, and a region of Newtonian attraction. Depending on the sign and value of the cosmological constant the solutions are asymptotically de Sitter (dS), asymptotically flat, or asymptotically anti-de Sitter (AdS).

gr-qc↗
arXiv2015

Entropy of an extremal electrically charged thin shell and the extremal black hole

There is a debate as to what is the value of the the entropy $S$ of extremal black holes. There are approaches that yield zero entropy $S=0$, while there are others that yield the Bekenstein-Hawking entropy $S=A_+/4$, in Planck units. There are still other approaches that give that $S$ is proportional to $r_+$ or even that $S$ is a generic well-behaved function of $r_+$. Here $r_+$ is the black hole horizon radius and $A_+=4πr_+^2$ is its horizon area. Using a spherically symmetric thin matter shell with extremal electric charge, we find the entropy expression for the extremal thin shell spacetime. When the shell's radius approaches its own gravitational radius, and thus turns into an extremal black hole, we encounter that the entropy is $S=S(r_+)$, i.e., the entropy of an extremal black hole is a function of $r_+$ alone. We speculate that the range of values for an extremal black hole is $0\leq S(r_+) \leq A_+/4$.

hep-th↗
arXiv2015

Thermodynamics of rotating thin shells in the BTZ spacetime

We investigate the thermodynamic equilibrium states of a rotating thin shell, i.e., a ring, in a (2+1)-dimensional spacetime with a negative cosmological constant. The inner and outer regions with respect to the shell are given by the vacuum anti-de Sitter and the rotating Bañados-Teitelbom-Zanelli spacetimes, respectively. The first law of thermodynamics on the thin shell, together with three equations of state for the pressure, the local inverse temperature and the thermodynamic angular velocity of the shell, yields the entropy of the shell, which is shown to depend only on its gravitational radii. When the shell is pushed to its own gravitational radius and its temperature is taken to be the Hawking temperature of the corresponding black hole, the entropy of the shell coincides with the Bekenstein-Hawking entropy. In addition, we consider simple ansätze for the equations of state, as well as a power-law equation of state where the entropy and the thermodynamic stability conditions can be examined analytically.

hep-th↗
arXiv2015

Rotating thin shells in (2+1)-dimensional asymptotically AdS spacetimes: Mechanical properties, Machian effects, and energy conditions

A rotating thin shell in a (2+1)-dimensional asymptotically AdS spacetime is studied. The spacetime exterior to the shell is the rotating BTZ spacetime and the interior is the empty spacetime with a cosmological constant. Through the Einstein equation in (2+1)-dimensions and the corresponding junction conditions we calculate the dynamical relevant quantities, namely, the rest energy-density, the pressure, and the angular momentum flux density. We also analyze the matter in a frame where its energy-momentum tensor has a perfect fluid form. In addition, we show that Machian effects, such as the dragging of inertial frames, also occur in rotating (2+1)-dimensional spacetimes. The weak and the dominant energy condition for these shells are discussed.

gr-qc↗
arXiv2015

Entropy of a self-gravitating electrically charged thin shell and the black hole limit

A static self-gravitating electrically charged spherical thin shell embedded in a (3+1)-dimensional spacetime is used to study the thermodynamic and entropic properties of the corresponding spacetime. Inside the shell, the spacetime is flat, outside it is Reissner-Nordström, and this establishes the energy density, the pressure, and the electric charge in the shell. Imposing that the shell is at a given local temperature and that the first law of thermodynamics holds on the shell one can find the integrability conditions for the temperature and for the thermodynamic electric potential, the thermodynamic equilibrium states, and the thermodynamic stability conditions. Through the integrability conditions and the first law of thermodynamics an expression for the shell's entropy can be calculated. It is found that the shell's entropy is a function of the shell's gravitational and Cauchy radii alone. A plethora of sets of temperature and electric potential equations of state can be given. One set of equations of state is related to the Hawking temperature and a precisely given electric potential. Then, as one pushes the shell to its own gravitational radius and the temperature is set precisely equal to the Hawking temperature, so that there is a finite quantum backreaction, one finds that the entropy of the shell equals the Bekenstein-Hawking entropy for a black hole. Other set of equations of state are given and the thermodynamic properties analyzed. Whatever the initial equation of state for the temperature, as the shell radius approaches its own gravitational radius, the quantum backreaction imposes the Hawking temperature for the shell in this limit. Thus, when the shell's radius is sent to the shell's own gravitational radius the formalism developed allows to find the precise form of the Bekenstein-Hawking entropy of the correlated black hole.

hep-th↗
arXiv2015

Newtonian wormholes with spherical symmetry and tidal forces on test particles

A spherically symmetric wormhole in Newtonian gravitation in curved space, enhanced with a connection between the mass density and the Ricci scalar, is presented. The wormhole, consisting of two connected asymptotically flat regions, inhabits a spherically symmetric curved space. The gravitational potential, gravitational field and the pressure that supports the fluid that permeates the Newtonian wormhole are computed. Particle dynamics and tidal effects in this geometry are studied. The possibility of having Newtonian black holes in this theory is sketched.

gr-qc↗
arXiv2015

Sharp bounds on the radius of relativistic charged spheres: Guilfoyle's stars saturate the Buchdahl-Andréasson bound

Buchdahl, by imposing a few physical assumptions on the matter, i.e., its density is a nonincreasing function of the radius and the fluid is a perfect fluid, and on the configuration, such as the exterior is the Schwarzschild solution, found that the radius $r_0$ to mass $m$ ratio of a star would obey the Buchdahl bound $r_0/m\geq9/4$. He noted that the bound was saturated by the Schwarzschild interior solution, the solution with $ρ_{\rm m}(r)= {\rm constant}$, where $ρ_{\rm m}(r)$ is the energy density of the matter at $r$, when the central central pressure blows to infinity. Generalizations of this bound have been studied. One generalization was given by Andréasson by including electrically charged matter and imposing that $p+2p_T \leqρ_{\rm m}$, where $p$ is the radial pressure and $p_T$ the tangential pressure. His bound is given by $r_0/m\geq9/\left(1+\sqrt{1+3\,q^2/r_0^2}\right)^{2}$, the Buchdahl-Andréasson bound, with $q$ being the star's total electric charge. Following Andréasson's proof, the configuration that saturates the Buchdahl bound is an uncharged shell, rather than the Schwarzschild interior solution. By extension, the configurations that saturate the Buchdahl-Andréasson bound are charged shells. One expects then, in turn, that there should exist an electrically charged equivalent to the interior Schwarzschild limit. We find here that this equivalent is provided by the equation $ρ_{\rm m}(r) + {Q^2(r)}/ {\left(8π\,r^4\right)}= {\rm constant}$, where $Q(r)$ is the electric charge at $r$. This equation was put forward by Cooperstock and de la Cruz, and Florides, and realized in Guilfoyle's stars. When the central pressure goes to infinity Guilfoyle's stars are configurations that saturate the Buchdahl-Andréasson bound. It remains to find a proof in Buchdahl's manner such that these configurations are the limiting configurations of the bound.

gr-qc↗
arXiv2015

Compact stars with a small electric charge: the limiting radius to mass relation and the maximum mass for incompressible matter

One of the stiffest equations of state for matter in a compact star is constant energy density and this generates the interior Schwarzschild radius to mass relation and the Misner maximum mass for relativistic compact stars. If dark matter populates the interior of stars, and this matter is supersymmetric or of some other type, some of it possessing a tiny electric charge, there is the possibility that highly compact stars can trap a small but non-negligible electric charge. In this case the radius to mass relation for such compact stars should get modifications. We use an analytical scheme to investigate the limiting radius to mass relation and the maximum mass of relativistic stars made of an incompressible fluid with a small electric charge. The investigation is carried out by using the hydrostatic equilibrium equation, i.e., the Tolman-Oppenheimer-Volkoff (TOV) equation, together with the other equations of structure, with the further hypothesis that the charge distribution is proportional to the energy density. The approach relies on Volkoff and Misner's method to solve the TOV equation. For zero charge one gets the interior Schwarzschild limit, and supposing incompressible boson or fermion matter with constituents with masses of the order of the neutron mass one gets that the maximum mass is the Misner mass. For a small electric charge, our analytical approximating scheme valid in first order in the star's electric charge, shows that the maximum mass increases relatively to the uncharged case, whereas the minimum possible radius decreases, an expected effect since the new field is repulsive aiding the pressure to sustain the star against gravitational collapse.

astro-ph.SR↗
arXiv2014

Newtonian wormholes

A wormhole solution in Newtonian gravitation, enhanced through an equation relating the Ricci scalar to the mass density, is presented. The wormhole inhabits a spherically symmetric curved space, with one throat and two asymptotically flat regions. Particle dynamics in this geometry is studied, and the three distinct dynamical radii, namely, the geodesic, circumferential, and curvature radii, appear naturally in the study of circular motion. Generic motion is also analysed. A limiting case, although inconclusive, suggests the possibility of having a Newtonian black hole in a region of finite (nonzero) size.

gr-qc↗
arXiv2014

Einstein-aether theory with a Maxwell field: General formalism

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.

gr-qc↗
arXiv2014

Incompressible relativistic spheres: Electrically charged stars, compactness bounds, and quasiblack hole configurations

We investigate the properties of relativistic star spheres made of an electrically charged incompressible fluid, generalizing, thus, the Schwarzschild interior solution. The investigation is carried by integrating numerically the hydrostatic equilibrium equation, i.e., the Tolman-Oppenheimer-Volkoff (TOV) equation, with the hypothesis that the charge distribution is proportional to the energy density. We match the interior to a Reissner-Nordström exterior, and study some features of these star spheres such as the total mass $M$, the radius $R$, and the total charge $Q$. We also display the pressure profile. For star spheres made of a perfect fluid there is the Buchdahl bound, $R/M\geq 9/4$, a compactness bound found from generic principles. For the Schwarzschild interior solution there is also the known compactness limit, the interior Schwarzschild limit where the configurations attain infinite central pressure, given by $R/M=9/4$, yielding an instance where the Buchdahl bound is saturated. We study this limit of infinite central pressure for the electrically charged stars and compare it with the Buchdahl-Andréasson bound, a limit that, like the Buchdahl bound for the uncharged case, is obtained by imposing some generic physical conditions on charged configurations. We show that the electrical interior Schwarzschild limit of all but two configurations is always below the Buchdahl-Andréasson limit, i.e., we find that the electrical interior Schwarzschild limit does not generically saturate the Buchdahl-Andréasson bound. We also find that the quasiblack hole limit, i.e., the extremal most compact limit for charged incompressible stars, is reached when the matter is highly charged and the star's central pressure tends to infinity. This is one of the two instances where the Buchdahl-Andréasson bound is saturated, the other being the uncharged, interior Schwarzschild solution.

gr-qc↗
arXiv2014

Entropy of thin shells in a (2+1)-dimensional asymptotically AdS spacetime and the BTZ black hole limit

The thermodynamic equilibrium states of a static thin ring shell in a (2+1)-dimensional spacetime with a negative cosmological constant are analyzed. Inside the ring, the spacetime is pure anti-de Sitter (AdS), whereas outside it is a Bañados-Teitelbom-Zanell$ (BTZ) spacetime and thus asymptotically AdS. The first law of thermodynamics applied to the thin shell, plus one equation of state for the shell's pressure and another for its temperature, leads to a shell's entropy, which is a function of its gravitational radius alone. A simple example for this gravitational entropy, namely, a power law in the gravitational radius, is given. The equations of thermodynamic stability are analyzed, resulting in certain allowed regions for the parameters entering the problem. When the Hawking temperature is set on the shell and the shell is pushed up to its own gravitational radius, there is a finite quantum backreaction that does not destroy the shell. One then finds that the entropy of the shell at the shell's gravitational radius is given by the Bekenstein-Hawking entropy.

gr-qc↗
arXiv2013

Rotating analogue black holes: Quasinormal modes and tails, superresonance, and sonic bombs and plants in the draining bathtub acoustic hole

The analogy between sound wave propagation and light waves led to the study of acoustic holes, the acoustic analogues of black holes. Many black hole features have their counterparts in acoustic holes. The Kerr metric, the rotating metric for black holes in general relativity, has as analogue the draining bathtub metric, a metric for a rotating acoustic hole. Here we report on the progress that has been made in the understanding of features, such as quasinormal modes and tails, superresonance, and instabilities when the hole is surrounded by a reflected mirror, in the draining bathtub metric. Given then the right settings one can build up from these instabilities an apparatus that stores energy in the form of amplified sound waves. This can be put to wicked purposes as in a bomb, or to good profit as in a sonic plant.

gr-qc↗
arXiv2013

Polytropic spheres with electric charge: compact stars, the Oppenheimer-Volkoff and Buchdahl limits, and quasiblack holes

We explore a class of compact charged spheres made of a charged perfect fluid with a polytropic equation of state. The charge density is chosen to be proportional to the energy density. The study is performed by solving the Tolman-Oppenheimer-Volkoff (TOV) equation which describes the hydrostatic equilibrium. We show the dependence of the structure of the spheres for several characteristic values of the polytropic exponent and for different values of the charge densities. We also study other physical properties of the charged spheres, such as the total mass, total charge, radius and sound speed and their dependence on the polytropic exponent. We find that for the polytropic exponent γ=4/3 the Chandrasekhar mass limit coincides with the Oppenheimer-Volkoff mass limit. We test the Oppenheimer-Volkoff limit for such compact objects. We also analyze the Buchdahl limit for these charged polytropic spheres, which happens in the limit of very high polytropic exponents, i.e., for a stiff equation of state. It is found that this limit is extremal and it is a quasiblack hole.

gr-qc↗
arXiv2013

Thermodynamics, entropy, and stability of thin shells in 2+1 flat spacetimes

The thermodynamic equilibrium states of a static thin ring shell in a (2+1)-dimensional flat spacetime is analyzed. Inside the ring the spacetime is flat, whereas outside it is conical flat. The first law of thermodynamics applied to the thin shell leads to a shell's entropy which is a function of its mass alone. Two simple forms for this mass function are given leading to two different expressions for the entropy. The equations of thermodynamic stability are analyzed resulting in certain allowed regions for the free parameters. Contrary to the usual (3+1)-dimensional case this shell's entropy is purely classic, as the only fundamental constant that enters into the problem is the (2+1)-dimensional gravitational constant $G_3$, which has units of inverse mass.

gr-qc↗