Bounds on spinning particles in their innermost stable circular orbits around rotating braneworld black hole

Abstract

We study the innermost stable circular orbit (ISCO) of a spinning test particle moving in the vicinity of an axially symmetric rotating braneworld black hole (BH). We start with the description of the event horizon, static limit surface and ergosphere region of such BH and bring out the effect of tidal charge parameter on ergosphere. It is found that the ISCO of rotating braneworld BH is very sensitive to braneworld BH deformation parameter C (also known as tidal charge parameter) in addition to its rotation parameter. We further discovered that the orbital radius of the spinning test particles changes non-monotonously with the braneworld BH deformation parameter. It is found that for rotating braneworld BH the allowed range of the particle spin grows as the tidal charge parameter C decreases, in contrast with the Kerr-Newman BH. We also found the similar behavior of the particle's spin for the braneworld Reissner-Nordström (C < 0) BH in contrast with its general relativity counterpart (i.e., Reissner-Nordström) having (C > 0).

Covariant version of the Pauli Hamiltonian, spin-induced noncommutativity, Thomas precession, and the precession of spin

“…In 1/c 2 -approximation our equations imply the equations (6) and (13). As we saw above, they also represent equations of motion of the Hamiltonian theory (18).…”

“…Excluding the conjugated momentum p from these equations, we arrive at the Lorentz-force equation (1). Equations (13) can also be obtained from the Hamiltonian (9), presented in terms of the physical variables x(t) and p(t). While in general reparametrization-invariant theory with Dirac constraints it requires some caution [32][33][34][35][36][37][38], the final result is very simple [40]: the physical Hamiltonian coincides with the right hand side of Eq.…”

“…One obscure point of this approach, which has been raised for discussion already in the pioneer works [1][2][3][4] and remains under debates up to date, is the so-called problem of covariant formalism. Clarification of this issue could be of interest in various areas, including muon and electron g − 2 -experiments [5][6][7][8], influence of spin on the trajectory of a rotating body in general relativity [9][10][11][12][13][14], and black hole physics near horizon [9,[15][16][17][18]. In the textbooks and reviews, it has become almost a tradition to discuss the problem without formulating it in an exact form 1 .…”

Motion of spinning particles in non asymptotically flat spacetimes

“…One can see from (17) that in order to have ( p r ) 2 ≥ 0, the energy of the particle must satisfy one of the following conditions:…”

“…All the theoretical models used to describe the observables obtained from accretion disks rely on the mathematical description of the motion of test particles and viscous plasma fluid in the surroundings of the black hole candidate. However, the motion of test particles may be influenced by a e-mail: bobir.toshmatov@nu.edu.kz (corresponding author) b e-mail: rahimov@astrin.uz c e-mail: ahmedov@astrin.uz d e-mail: daniele.malafarina@nu.edu.kz a large number of factors, including, for example, the geometry [5][6][7][8], the presence of external fields [9,10], the spin of the particles [11][12][13][14][15] and possible deviations from classical general relativity [16,17].…”