arXiv subjects

Gonçalo M. Quinta

Publications and source records attributed to Gonçalo M. Quinta.

22 records · Page 2Linked to original sources

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

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↗

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

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↗