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Register a new userNegative specific heat of black-holes from Fluid-Gravity Correspondence
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Added by
Swastik Bhattacharya
Publication date
2017
fields
Physics
and research's language is
English
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Black-holes in asymptotically flat space-times have negative specific heat --- they get hotter as they loose energy. A clear statistical mechanical understanding of this has remained a challenge. In this work, we address this issue using fluid-gravity correspondence which aims to associate fluid degrees of freedom to the horizon. Using linear response theory and the teleological nature of event horizon, we show explicitly that the fluctuations of the horizon-fluid lead to negative specific heat for Schwarzschild black Hole. We also point out how the specific heat can be positive for Kerr-Newman or AdS black holes. Our approach constitutes an important advance as it allows us to apply canonical ensemble approach to study thermodynamics of asymptotically flat black-hole space-times.
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We study quasinormal modes of black holes in Lovelock gravity. We formulate the WKB method adapted to Lovelock gravity for the calculation of quasinormal frequencies (QNFs). As a demonstration, we calculate various QNFs of Lovelock black holes in seven and eight dimensions. We find that the QNFs show remarkable features depending on the coefficients of the Lovelock terms, the species of perturbations, and spacetime dimensions. In the case of the scalar field, when we increase the coefficient of the third order Lovelock term, the real part of QNFs increases, but the decay rate becomes small irrespective of the mass of the black hole. For small black holes, the decay rate ceases to depend on the Gauss-Bonnet term. In the case of tensor type perturbations of the metric field, the tendency of the real part of QNFs is opposite to that of the scalar field. The QNFs of vector type perturbations of the metric show no particular behavior. The behavior of QNFs of the scalar type perturbations of the metric field is similar to the vector type. However, available data are rather sparse, which indicates that the WKB method is not applicable to many models for this sector.
An exact and regular solution, describing a couple of charged and spinning black holes, is generated in an external electromagnetic field, via Ernst technique, in Einstein-Maxwell gravity. A wormhole instantonic solution interpolating between the two black holes is constructed to discuss, at the semi-classical level, the quantum process of creation rate, in an external magnetic field, of this charged and spinning black hole pair.
With the successes of $f(R)$ theory as a neutral modification of Einsteins general relativity (GR), we continue our study in this field and attempt to find general natural and charged black hole (BH) solutions. In the previous papers cite{Nashed:2020mnp,Nashed:2020tbp}, we applied the field equation of the $f(R)$ gravity to a spherically symmetric space-time $ds^2=-U(r)dt^2+frac{dr^2}{V(r)}+r^2 left( dtheta^2+sin^2theta dphi^2 right)$ with unequal metric potentials $U(r)$ and $V(r)$ and with/without electric charge. Then we have obtained equations which include all the possible static solutions with spherical symmetry. To ensure the closed form of system of the resulting differential equations in order to obtain specific solutions, we assumed the derivative of the $f(R)$ with respect to the scalar curvature $R$ to have a form $F_1(r)=frac{df(R(r))}{dR(r)} propto frac{c}{r^n}$ but in case $n>2$, the resulting black hole solutions with/without charge do not generate asymptotically GR BH solutions in the limit $crightarrow 0$ which means that the only case that can generate GR BHs is $n=2$. In this paper, we assume another form, i.e., $F_1(r)= 1-frac{F_0-left(n-3right)}{r^n}$ with a constant $F_0$ and show that we can generate asymptotically GR BH solutions for $n>2$ but we show that the $n=2$ case is not allowed. This form of $F_1(r)$ could be the most acceptable physical form that we can generate from it physical metric potentials that can have a well-known asymptotic form and we obtain the metric of the Einstein general relativity in the limit of $F_0to n-3$. We show that the form of the electric charge depends on $n$ and that $n eq 2$. Our study shows that the power $n$ is sensitive and why we should exclude the case $n=2$ for the choice of $F_1(r)$ presented in this study.
The open question of whether a Kerr black hole can become tidally deformed or not has profound implications for fundamental physics and gravitational-wave astronomy. We consider a Kerr black hole embedded in a weak and slowly varying, but otherwise arbitrary, multipolar tidal environment. By solving the static Teukolsky equation for the gauge-invariant Weyl scalar $psi_0$, and by reconstructing the corresponding metric perturbation in an ingoing radiation gauge, for a general harmonic index $ell$, we compute the linear response of a Kerr black hole to the tidal field. This linear response vanishes identically for a Schwarzschild black hole and for an axisymmetric perturbation of a spinning black hole. For a nonaxisymmetric perturbation of a spinning black hole, however, the linear response does not vanish, and it contributes to the Geroch-Hansen multipole moments of the perturbed Kerr geometry. As an application, we compute explicitly the rotational black hole tidal Love numbers that couple the induced quadrupole moments to the quadrupolar tidal fields, to linear order in the black hole spin, and we introduce the corresponding notion of tidal Love tensor. Finally, we show that those induced quadrupole moments are closely related to the well-known physical phenomenon of tidal torquing of a spinning body interacting with a tidal gravitational environment.
We discuss the merger process of binary black holes with Hawking radiation taken into account. Besides the redshifted radiation to infinity, binary black holes can exchange radiation between themselves, which is first redshifted and then blueshifted when it propagates from one hole to the other. The exchange rate should be large when the temperature-divergent horizons are penetrating each other to form a single horizon with unique temperature. This will cause non-negligible mass and angular momentum transfer between the black holes during the merging process of the horizons. We further argue in the large mass ratio limit that the light hole whose local evaporation is enhanced by the competing redshift-blueshift effects will probably evaporate or decay completely before reaching the the horizon of the heavy one. We also discuss the possibility of testing Hawking radiation and even exploring the information loss puzzle in gravitational wave observations.
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