We present the Spectroscopic Time-Resolving Observatory for Broadband Energy X-rays (STROBE-X), a probe-class mission concept selected for study by NASA. It combines huge collecting area, high throughput, broad energy coverage, and excellent spectral and temporal resolution in a single facility. STROBE-X offers an enormous increase in sensitivity for X-ray spectral timing, extending these techniques to extragalactic targets for the first time. It is also an agile mission capable of rapid response to transient events, making it an essential X-ray partner facility in the era of time-domain, multi-wavelength, and multi-messenger astronomy. Optimized for study of the most extreme conditions found in the Universe, its key science objectives include: (1) Robustly measuring mass and spin and mapping inner accretion flows across the black hole mass spectrum, from compact stars to intermediate-mass objects to active galactic nuclei. (2) Mapping out the full mass-radius relation of neutron stars using an ensemble of nearly two dozen rotation-powered pulsars and accreting neutron stars, and hence measuring the equation of state for ultradense matter over a much wider range of densities than explored by NICER. (3) Identifying and studying X-ray counterparts (in the post-Swift era) for multiwavelength and multi-messenger transients in the dynamic sky through cross-correlation with gravitational wave interferometers, neutrino observatories, and high-cadence time-domain surveys in other electromagnetic bands. (4) Continuously surveying the dynamic X-ray sky with a large duty cycle and high time resolution to characterize the behavior of X-ray sources over an unprecedentedly vast range of time scales. STROBE-Xs formidable capabilities will also enable a broad portfolio of additional science.
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