MG15 - Talk detail

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It has been shown by explicit and exact calculation that the geometric product formula i.e. area (or entropy) product formula of outer horizon (OH) and inner horizon (IH) for charged accelerating black hole (BH) should \emph{ neither be mass-independent nor it be quantized}. This implies that the area (or entropy ) product is mass-independent conjecture has been \emph{broken down} for charged accelerating BH. This also further implies that the mass-independent feature of the area product of OH and IH is \emph{not} a generic feature at all. We also compute that the \emph{Cosmic-Censorship-Inequality} for this BH. Moreover, we compute the specific heat for this BH to determine the local thermodynamic stability of this BH. Under certain criterion, the BH shows the second order phase transition. Furthermore, we compute logarithmic corrections to the entropy for the said BH due to small statistical fluctuations around the thermal equilibrium.

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We have examined the thermodynamic properties for a variety of spherically symmetric charged-AdS black hole (BH) solutions, including the charged AdS BH surrounded by quintessence dark energy and charged AdS BH in f(R) gravity in \emph{extended phase-space}. This framework involves treating the cosmological constant as thermodynamic variable (for example: thermodynamic pressure and thermodynamic volume). Then they should behave as an analog of Van der Waal (VdW) like systems. In the extended phase space we have calculated the \emph{entropy product} and \emph{thermodynamic volume product} of all horizons. The mass (or enthalpy) independent nature of the said product signals they are \emph{universal} quantities. %Various type of phase diagram of the specific heat has been drawn. The divergence of the specific heat indicates that the second order phase transition occurs under certain condition. In the appendix-A, we have studied the thermodynamic volume products for axisymmetric spacetime and it is shown to be \emph{not universal} in nature.

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We study the thermodynamic properties of inner and outer horizons of scalar-tensor-vector gravity (STVG) or modified gravity (MG) and its consequences on the holographic duality. We derive the thermodynamic product formula for this gravity. We consider both spherically symmetric solution and axisymmetric solution of MG. We find that the area product formula for both cases is \emph{not} mass-independent because they depends on ADM mass parameter while in Einstein gravity this formula is mass-independent. We also examine the \emph{first law} is fulfilled at the inner horizon (IH) as well as outer horizon (OH). We also derive other thermodynamic products and sums. We further derive the Smarr like mass formula for this kind of black hole (BH) in MG. Moreover, we derive the area bound for both the horizons. Furthermore, we show that the central charges of the left and right moving sectors are same via universal thermodynamic relations. Finally, we derive the mass-independent area product combinations for regular MG BH.

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We compute the area(or entropy) product formula for a regular black hole derived by Ay\'on-Beato and Garc\'ia in 1998\cite{abg}. By explicit and exact calculation, it is shown that the entropy product formula of two physical horizons strictly \emph{depends} upon the ADM mass parameter that means it is \emph{not} an universal(mass-independent) quantity. But a slightly more complicated function of event horizon area and Cauchy horizon area is indeed a \emph{mass-independent} quantity. We also compute other thermodynamic properties of the said black hole. We further study the stability of such black hole by computing the specific heat for both the horizons. It has been observed that under certain condition the black hole possesses second order phase transition. The pictorial diagram of the phase transition is given.

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We present a detailed study of the circular geodesic motion of neutral test particles on the equatorial plane of a spherically symmetric scalarized \emph{neutron star}~(NS). We also examined the stability criteria for massive and massless particles for the said NS by computing the effective potential. We compute the radii of innermost stable circular orbit~(ISCO), marginally bound circular orbit~(MBCO) and circular photon orbit~(CPO). We also derive the \emph{Paczy\'{n}ski-Witta potential} which is so called the \emph{pseudo-Newtonian potential} which is very crucial to analyze the accretion disk properties. By analyzing the null circular geodesics we compute the Lyapunov exponent for the scalarized NS. Moreover, we show that in the \emph{eikonal limit}, the real and imaginary parts of the quasi normal modes~(QNM) of the scalarized NS could be determined in terms of the frequency of the NS and instability time scale of the \emph{unstable circular photon geodesics}. Furthermore, we study the Ba\~{n}ados, Silk and West~(BSW) effect of this scalarized NS. We find that the center-of-mass~(CM) energy of colliding neutral test particles near the surface of the NS have the finite energy.

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