  We present the expected observational properties of a general relativistic
instability supernova (GRSN) from the 55,500 Msun primordial (Population III)
star. Supermassive stars exceeding 1e4 Msun may exist in the early Universe.
They are generally considered to collapse through the general relativistic
instability to be seed black holes to form supermassive (~ 1e9 Msun) black
holes observed as high-redshift quasars. Some of them, however, may explode as
GRSNe if the explosive helium burning unbinds the supermassive stars following
the collapse triggered by the general relativistic instability. We perform the
radiation hydrodynamics simulation of the GRSN starting shortly before the
shock breakout. We find that the GRSN is characterized by a long-lasting (550
d) luminous (1.5e44 erg/s) plateau phase with the photospheric temperature of
around 5000 K in the rest frame. The plateau phase lasts for decades when it
appears at high redshifts and it will likely be observed as a persistent source
in the future deep near-infrared imaging surveys. Especially, the near-infrared
images reaching 29 AB magnitude that can be obtained by Galaxy and Reionization
EXplorer (G-REX) and James Webb Space Telescope (JWST) allow us to identify
GRSNe up to z ~ 15. Deeper images enable us to discover GRSNe at even higher
redshifts. Having extremely red color, they can be distinguished from other
persistent sources such as high-redshift galaxies by using color information.
We conclude that the deep near-infrared images are able to constrain the
existence of GRSNe from the primordial supermassive stars in the Universe even
without the time domain information.
