We study the Schwarzschild and Reissner-Nordström black hole thermodynamics using the simplest form of the generalized uncertainty principle (GUP) proposed in the literature. The expressions for the mass-temperature relation, heat capacity and entropy are obtained in both cases from which the critical and remnant masses are computed. Our results are exact and reveal that these masses are identical and larger than the so called singular mass for which the thermodynamics quantities become ill-defined. The expression for the entropy reveals the well known area theorem in terms of the horizon area in both cases upto leading order corrections from GUP. The area theorem written in terms of a new variable which can be interpreted as the reduced horizon area arises only when the computation is carried out to the next higher order correction from GUP.Various theories of quantum gravity have suggested the need of an observer-independent minimum length scale. A minimal length expected to be close or equal to the Planck length occurs in string theory [1], noncommutative geometry [2], to name a few. One of the manifestations of the inclusion of a minimal length in these theories is the generalized uncertainty principle (GUP). This idea, first proposed in [3] has recently been considered seriously to study black hole thermodynamics [4]-[6] and its quantum corrected entropy [7]-[9], compute quantum gravity corrections in quantum systems (such as particle in a box, Landau levels, simple harmonic oscillator, etc.) [10]-[15], compute Planck scale corrections to the phenomena of superconductivity and quantum Hall effect [16] and to understand its consequences in cosmology [17], [18]. In this paper, we shall study the thermodynamic properties of the Schwarzschild and Reissner-Nordström (RN) black holes using the simplest form of the GUP proposed in * sunandan

In this paper, we calculate the modification to the thermodynamics of a Schwarzschild black hole in higher dimensions because of Generalized Uncertainty Principle (GUP). We use the fact that the leading order corrections to the entropy of a black hole has to be logarithmic in nature to restrict the form of GUP. We observe that in six dimensions, the usual GUP produces the correct form for the leading order corrections to the entropy of a black hole. However, in five and seven dimensions a linear GUP, which is obtained by a combination of DSR with the usual GUP, is needed to produce the correct form of the corrections to the entropy of a black hole. Finally, we demonstrate that in five dimensions, a new form of GUP containing quadratic and cubic powers of the momentum also produces the correct form for the leading order corrections to the entropy of a black hole.

In this paper, we investigate the thermodynamic properties of black holes in the framework of rainbow gravity. By considering rainbow functions in the metric of Schwarzschild and Reissner-Nordström black holes, remnant and critical masses are found to exist. Demanding the universality of logarithmic corrections to the semiclassical area law for the entropy leads to constraining the form of the rainbow functions. The mass output and the radiation rate for these constrained form of rainbow functions have been computed for different values of the rainbow parameter η and have striking similarity to those derived from the generalized uncertainty principle.

In this paper, we study the thermodynamics of black holes using a generalized uncertainty principle (GUP) with a correction term linear order in the momentum uncertainty. The mass-temperature relation and heat capacity are calculated from which critical and remnant masses are obtained. The results are exact and are found to be identical. The entropy expression gives the famous area theorem upto leading order corrections from GUP. In particular, the linear order term in GUP leads to a √ A correction to the area theorem. Finally, the area theorem can be expressed in terms of a new variable termed as reduced horizon area only when the calculation is done to the next higher order correction from GUP.The idea of existence of a minimal length arises naturally in quantum gravity theories in the form of effective minimal uncertainty in position. For example, in string theory, it is impossible to improve the spatial resolution below the characteristic length of the string which is expected to be close or equal to Planck length. Based on these arguments, the conventional Heisenberg uncertainty principle has been modified to the generalized uncertainty principle (GUP) [3], [4]. This idea, proposed first in [5], has led recently to a considerable amount of study in various areas of physics. For instance, the laws of black hole thermodynamics [6]- [8] has been investigated under this modification [9]-[12], quantum gravity corrections are computed in quantum systems (such as particle in a box, Landau levels and simple harmonic oscillator) [13]-[17], Planck scale corrections are obtained in the phenomena of superconductivity and quantum Hall effect [18] and its implications has been studied in cosmology [19], [20].In this paper, we will find the thermodynamic properties of the Schwarzschild and Reissner-Nordström (RN) black holes using the following form of the GUP proposed in *

We study the modification of thermodynamic properties of Schwarzschild and Reissner-Nordström black hole in the framework of generalized uncertainty principle with correction terms up to fourth order in momentum uncertainty. The mass-temperature relation and the heat capacity for these black holes have been investigated. These have been used to obtain the critical and remnant masses. The entropy expression using this generalized uncertainty principle reveals the area law up to leading order logarithmic corrections and subleading corrections of the form 1/ . The mass output and radiation rate using Stefan-Boltzmann law have been computed which show deviations from the standard case and the case with the simplest form for the generalized uncertainty principle.