On Effective Potential in Tortoise Coordinate

Abstract

In this paper, we study the field dynamics in Tortoise coordinate where the equation of motion of a scalar can be written as Schrodinger-like form. We obtain a general form for effective potential by finding the Schrodinger equation for scalar and spinor fields and study its global behavior in some black hole backgrounds in three dimension such as BTZ black holes, new type black holes and black holes with no horizon.Especially, we study the asymptotic behavior of potential at infinity, horizons and origin and find that its asymptotic in BTZ and new type solution is completely different from that of vanishing horizon solution. In fact, potential for vanishing horizon goes to a fixed quantity at infinity, while in BTZ and new type black hole we have an infinite barrier.

Exact radial solution in 2+1 gravity with a real scalar field

“…As a closing note let us briefly mention that quite recently, several papers appeared which are related to different other aspects of the study of (2 + 1)-dimensional gravity: In [25] and [26], massive gravity and supergravity are discussed; in [27], higher spin in topologically massive gravity is discussed; in [28] and [29] wormholes and star models are constructed in 2 + 1 dimensions; in [30], Birkhoff's theorem is generalized; in [31][32][33][34][35][36][37][38] various properties of the BTZ geometry are discussed; in [39], massive particles with spin in 2 + 1 dimension are constructed; in [40][41][42][43][44] further aspects of (2 + 1)-dimensional gravity are deduced and discussed; and finally in [45], the observability of strong gravitational sources (black hole, naked singularities) via lensing is discussed.…”

Exact radial solution in 2+1 gravity with a real scalar field

“…As a closing note let us briefly mention that quite recently, several papers appeared which are related to different other aspects of the study of (2 + 1)-dimensional gravity: In [25] and [26], massive gravity and supergravity are discussed; in [27], higher spin in topologically massive gravity is discussed; in [28] and [29] wormholes and star models are constructed in 2+1 dimensions; in [30], Birkhoff's theorem is generalized; in [31], [32], [33], [34], [35], [36], [37], and [38] various properties of the BTZ geometry are discussed; in [39], massive particles with spin in 2 + 1 dimension are constructed; in [40], [41], [42], [43], and [44] further aspects of (2 + 1)-dimensional gravity are deduced and discussed; and finally in [45], the observability of strong gravitational sources (black hole, naked singularities) via lensing is discussed.…”