Tao Zhu

Focusing on a Schwarzschild spacetime modified by loop quantum gravity holonomy corrections, this work explores the gravitational radiation produced by test masses in bound periodic configurations. The underlying geometry incorporates a quantum-correction parameter q c that alters the radial metric scaling while maintaining both asymptotic flatness and the classical horizon radius. The bound geodesics are systematically classified using the zoom–whirl representation labeled by three integers ( z , w , v ) . Gravitational waveforms are computed within a numerical framework that combines exact geodesic motion with the quadrupole approximation, which is suitable for extreme mass ratio inspirals. We demonstrate that the quantum corrections lead to distinct phase shifts, amplitude variations, and modifications to the harmonic structure of the waveforms, with increasingly complex features for orbits with larger zoom numbers. The corresponding frequency spectra and characteristic strain peak, which fall within the millihertz band, are within the sensitivity ranges of space-based detectors such as LISA, Taiji, and TianQin. For specific orbital configurations and values of the quantum-correction parameter, the characteristic strain exceeds the projected detector noise, indicating potential observability. Our results demonstrate that gravitational waves from periodic orbits provide a sensitive probe of quantum-corrected black hole spacetimes in the strong-field regime.

In scalar–tensor–vector gravity (STVG, also known as MOG), a massive vector field ϕ _μ generates a repulsive fifth force that endows rotating black holes with a gravitational charge Q ∝ α M , modifying the near-horizon geometry through a single deformation parameter α . We investigate how this vector-field coupling imprints itself on the thermal continuum emission of geometrically thin, optically thick accretion disks in the Kerr-MOG black hole. By rederiving the innermost stable circular orbit (ISCO), the Novikov–Thorne radiative flux, the relativistic energy shift, and the null geodesic structure for the Kerr-MOG spacetime, we compute fully relativistic disk spectra across a broad range of spins, inclinations, and fifth-force strengths using a dedicated xspec spectral model ( kmspec ). We find that the fifth-force charge pushes the ISCO outward, lowers the peak disk temperature, and systematically softens the thermal continuum relative to its Kerr black hole counterpart at the same spin, with the deviation amplified at high observer inclinations. The resulting spectral modification closely mimics a reduction of spin in the pure Kerr black hole framework, indicating that independent spin measurements from, e.g., iron-line reflection spectroscopy are indispensable for disentangling the vector-field contribution. All results recover the standard Kerr black hole predictions when α = 0, and the model is validated against independent analytic and numerical benchmarks to machine precision. Application to a 69.6 ks XMM-Newton observation of LMC X-1 yields α < 0.044 at 90% confidence, consistent with the Kerr metric and general relativity.

Context. Broad and skewed iron K α emission lines in the X-ray spectra of accreting black holes encode key information about space-time geometry in the innermost disk regions. While relativistic reflection models that assume the Kerr metric have yielded spin measurements for dozens of black hole candidates, horizonless alternatives, particularly traversable “Kerr-like” wormholes, can reproduce many observational signatures of black holes and thus challenge the interpretation of these data. Aims. We aim to develop and apply a new relativistic reflection framework that explicitly incorporates Kerr-like wormhole geometries to predict the iron line distortions introduced by wormhole throat effects and assess the feasibility of distinguishing event horizons from horizonless throats using current and future X-ray observations. Methods. Building on a custom ray-tracing subroutine for Kerr-like wormhole space-times, we implemented two custom XSPEC modules, kwline for isolated δ -function line profiles and kwconv for full rest-frame reflection spectra, parameterized by spin, throat radius, and shape-function coefficients. We computed a dense grid of line profiles over the wormhole parameter space, embedded them within multicomponent reflection models, and generated synthetic Nuclear Spectroscopic Telescope Array ( NuSTAR ) spectra that incorporate realistic response matrices and backgrounds. By fitting these simulated data with canonical Kerr black hole based models and examining fit quality and residual structure, we quantified the deviations attributable to wormhole geometries. Results. We find that Kerr-like wormholes systematically produce narrower Fe K α lines with suppressed red wings and angle-dependent morphological shifts as the throat parameter, λ , increases. In spectral fitting simulations of a high-flux 50 ks NuSTAR exposure (mocked with λ = 0.9, a _* = 0.998), standard Kerr black hole convolution models ( kerrconv ) can effectively mimic the wormhole spectrum with high statistical precision. Conversely, fitting with the self-consistent, angle-dependent reflection model relxillCp results in a formal statistical failure with pronounced structured residuals and unphysical parameter pegging, such as the emissivity index q _in reaching its limit of 10. These results indicate that while Kerr-like wormholes and black holes exhibit significant observational degeneracy under simple convolutional modeling, they can be distinguished through more rigid, self-consistent reflection frameworks. Conclusions. We conclude that large-throat wormholes are potentially detectable in high-quality X-ray spectra, provided the analysis moves beyond post-processing approximations toward fully consistent relativistic reflection models.